{
  "id": 5324,
  "curve_key": "0:449340624072",
  "ainvs": [
    "0",
    "0",
    "1",
    "0",
    "-520070167"
  ],
  "rank_lower_bound": 4,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell",
    "cubesum"
  ],
  "naive_height": 53.66209413059689,
  "faltings_height": 2.5294970866747026,
  "conductor": "168502734027",
  "bad_primes": [
    "3",
    "17",
    "1549"
  ],
  "discriminant": "-116844326644337052003",
  "regulator": "1088.296915546363889203286389249271475784962499",
  "points": [
    [
      "1549",
      "56538"
    ],
    [
      "20137/4",
      "2851705/8"
    ],
    [
      "196723/9",
      "87251284/27"
    ],
    [
      "29091769/18225",
      "146535626647/2460375"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cube-sum curve x^3 + y^3 = 236997 (Weierstrass model y^2 = x^3 - 432k^2, minimal model shown). Found in an exhaustive scan of cube-free k <= 7*10^5 by minimal-model naive height, with a Mestre-Nagao a_p sieve (p = 1 mod 3) and PARI ellrank 2-descent; companion to #5313 (k = 111690).",
  "created_at": "2026-10-21 13:09:18",
  "updated_at": "2026-10-21 13:09:18"
}